Find each product or quotient where possible. See Example 2.-5⁄2 ( 12⁄15 )

Verified step by step guidance

1. Identify the operation: This problem involves multiplying two fractions: \(-\frac{5}{2}\) and \(\frac{12}{15}\).
2. Multiply the numerators: Multiply the numerator of the first fraction by the numerator of the second fraction, i.e., \(-5 \times 12\).
3. Multiply the denominators: Multiply the denominator of the first fraction by the denominator of the second fraction, i.e., \(2 \times 15\).
4. Simplify the resulting fraction: After performing the multiplication, simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator and divide both by this number.
5. Check the sign: Since one of the fractions is negative, the product will be negative.

Key Concepts

Multiplication of Fractions

To multiply fractions, you multiply the numerators together and the denominators together. For example, to multiply -5/2 by 12/15, you calculate (-5 * 12) for the numerator and (2 * 15) for the denominator, resulting in a new fraction that can be simplified.

Simplifying Fractions

Simplifying fractions involves reducing them to their lowest terms by dividing both the numerator and the denominator by their greatest common divisor (GCD). For instance, in the product of -5/2 and 12/15, after multiplying, you can simplify the resulting fraction by finding the GCD of the numerator and denominator.

Division of Fractions

Dividing fractions requires multiplying by the reciprocal of the divisor. For example, to divide -5/2 by 12/15, you would multiply -5/2 by the reciprocal of 12/15, which is 15/12. This process also involves simplifying the resulting fraction as needed.